Eur. Phys. J. B (2014) 87: 49
https://doi.org/10.1140/epjb/e2014-40652-1

Regular Article

LMG model: Markovian evolution of classical and quantum correlations under decoherence

¹ Department of Engineering Science, University of Tehran, 11365-4563 Tehran, Islamic Republic of Iran
² Department of Physics, Shahed University, Tehran, Islamic Republic of Iran

^a e-mail: naymajd@ut.ac.ir

Received: 7 July 2013
Received in final form: 30 December 2013
Published online: 3 March 2014

Abstract

We have investigated the quantum phase transition in the ground state of collective Lipkin-Meshkov-Glick model (LMG model) subjected to decoherence due to its interaction, represented by a quantum channel, with an environment. We discuss the behavior of quantum and classical pair wise correlations in the system, with the quantumness of correlations measured by quantum discord (QD), entanglement of formation (EOF), measurement-induced disturbance (MID) and the Clauser-Horne-Shimony-Holt-Bell function (CHSH-Bell function). The time evolution established by system-environment interactions is assumed to be Markovian in nature and the quantum channels studied include the amplitude damping (AD), phase damping (PD), bit-flip (BF), phase-flip (PF), and bit-phase-flip (BPF) channels. One can identify appropriate quantities associated with the dynamics of quantum correlations signifying quantum phase transition in the model. Surprisingly, the CHSH-Bell function is found to detect all the phase transitions, even when quantum and classical correlations are zero for the relevant ground state.